Abstract
We provide strong evidence that the asymptotically free (1+1)-dimensional nonlinear O(3) sigma model can be regularized using a quantum lattice Hamiltonian, referred to as the "Heisenberg comb," that acts on a Hilbert space with only two qubits per spatial lattice site. The Heisenberg comb consists of a spin-half antiferromagnetic Heisenberg chain coupled antiferromagnetically to a second local spin-half particle at every lattice site. Using a world-line MonteCarlo method, we show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200000 in lattice units and argue how the continuum limit could emerge. We provide a quantum circuit description of the time evolution of the model and argue that near-term quantum computers may suffice to demonstrate asymptotic freedom.
Highlights
Formulating quantum field theories (QFTs) so that they can be implemented on a quantum computer has become an active area of research recently [1,2,3,4,5,6,7,8,9,10]
One of the first steps in this process is to construct a suitable lattice quantum Hamiltonian that acts on a Hilbert space realized by n qubits at each lattice site where n is small
Universality suggests that long distance physics can often be preserved at critical points after truncation if the symmetries of the model are preserved
Summary
Formulating quantum field theories (QFTs) so that they can be implemented on a quantum computer has become an active area of research recently [1,2,3,4,5,6,7,8,9,10]. The procedure of constructing a n-qubit lattice Hamiltonian for studying a QFT can be viewed as an extra regularization necessary for quantum computation and was referred to as the “qubit regularization” of the QFT in Refs. As with any form of regularization, a procedure to define the continuum limit of the n-qubit model is necessary.
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